I like the criticism of the story, but personally I disagree. I think it blends with the gameplay well, despite being separated. This was the first game I've played in years where I found myself wanting to read on and figure out more pieces of the puzzle (that being the plot, not the more literal puzzles)
Videogames have an inherent flaw in story telling in that they're supposed to be interactive, and have to take breaks from their purpose (fun game playing) to tell you of their "purpose" (the reason why the game environment/characters/powers/etc exist)
I think braid works well with this flaw in that it doesnt attempt a rigid story to explain anything, but instead uses the story to create a relationship with your character tim, and develop more of a feeling than anything. Which works well with the interaction of playing a game.
Also, I think you might be too rooted in the physical looking at your princess metaphors, it has a much more spiritual/universal sense to me personally, I feel like she's more of a symbol of thought, or creativity, or god, or inspiration, or nature. Basically, that thing that drives tim, and tim is us. the whole conveying the human condition through metaphor thing
still, I understand the criticism of its implementation and lack of finite explanations of itself. I just disagree with your view of jon's intentions (ie the analogy of a bad joke and noone laughing)